Most companies worry about 4 types of crimes: violence, sex, drugs, stealing or financial crimes. If their employee repeats any of those crimes on the job, then the company can be sued and destroyed by the costs. The cost will certainly be much more than the value of the employee.
More often now, companies will run an annual background check on established employees just to find out about employees that are going bad.
Nockahate9 has cause to be worried. You can run your own background check by looking at the county government's website in your county. Some online companies do employment background search that give much more information, such as reference checks, address history, criminal records, backruptcies, law suits, tax liens, sex offender registry, terrorist watch list.